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Abstract

Motivated by results from heavy-ion collisions we investigate the lower particle number limit of the applicability of fluid dynamics. We model the expansion of ultracold atoms in two dimensions suited to study this question experimentally and successfully predict the qualitative scaling of the elliptic flow with the particle number. For a fluid released from a harmonic trap with fluid static initial conditions, the dynamics can be reduced to ordinary differential equations by using Lagrange coordinates and solved for specific cases. Finding discrepancies between these results and experiments, we simulate the ideal fluid evolution of initial conditions fitted to experimental data, which shows that a system of ten strongly interacting 6Li atoms behaves like a fluid at early times of the expansion. The second problem addressed in this thesis is the non-perturbative prediction of shear viscosity for a real scalar quantum field theory with quartic interaction. We formulate the shear viscosity as a derivative of the quantum effective action and employ functional renormalization group methods to go beyond the perturbative regime. We construct a minimal ansatz and formulate flow equations for all free parameters. In the current form this leads to a trivial prediction for the shear viscosity which can be remedied by small changes to the interaction.